The relatively pure waxy and paraffinic hydrocarbons synthesized by the Fischer-Tropsch process are excellent sources of diesel fuel, jet fuel and premium lubricant oils with low sulfur, nitrogen and aromatics. When produced by a cobalt catalyst, the sulfur, nitrogen and aromatics content of the waxy hydrocarbons is essentially nil and they can therefore be passed to upgrading operations without prior hydrogen treatment. In a Fischer-Tropsch hydrocarbon synthesis process, a synthesis gas comprising H2 and CO is fed into a hydrocarbon synthesis reactor, in which the H2 and CO react in the presence of a Fischer-Tropsch catalyst to produce waxy hydrocarbons. The waxy hydrocarbon fraction that is liquid at the synthesis reaction conditions and solid at ambient room temperature and pressure conditions, is referred to as Fischer-Tropsch wax, and typically includes hydrocarbons boiling in both the fuels and lubricant oil ranges. However, these fuel and lubricant fractions have cloud and pour points too high to be useful as fuels and lubricant oils and must therefore be further processed (e.g., dewaxed), to acceptably low cloud and pour points. Fischer-Tropsch synthesis using a non-shifting cobalt catalyst produces more of the higher molecular weight hydrocarbons boiling in the lubricant range, than does a shifting catalyst, such as iron. Various processes have been disclosed for catalytically dewaxing these and other waxy hydrocarbons. Some, such as those employing a ZSM-5 catalyst, dewax by hydrocracking the waxy hydrocarbons to products boiling below the lubricant oil range. This results in a substantial loss of lubricant and higher boiling fuel, with concomitant low product yield. Others hydrorefine the wax to remove sulfur, nitrogen, oxygen containing molecules (oxygenates) and aromatics prior to dewaxing, to reduce deactivation of the dewaxing catalyst. The problem of high conversion and concomitant low product yield is exacerbated, when dewaxing a waxy, heavy lubricant oil fraction to an acceptable cloud point. Illustrative, but nonlimiting examples of various catalytic dewaxing processes are disclosed in, for example, U.S. Pat. Nos. 6,179,994; 6,090,989; 6,080,301; 6,051,129; 5,689,031 and 5,075,269 and EP 0 668 342 B1. There is still a need for a process that will produce acceptable yields of both fuels and lubricant base stocks, including a heavy lubricant base stock, from Fischer-Tropsch wax.